We report here an unusual ferroelectric to ferroelectric isostructural phase transition and associated giant negative thermal expansion (NTE) for the tetragonal composition x = 0.31 closest to the morphotropic phase boundary (MPB) of the multiferroic (1–x)BiFeO3–xPbTiO3 (BF-xPT) solid solution system. It is shown that the room temperature tetragonal phase (T1) of BF-0.31PT with extremely large tetragonality undergoes a first-order isostructural phase transition to another tetragonal phase (T2) with lower tetragonality without losing the P4mm space group symmetry and the occupied Wyckoff positions. The T2 phase finally transforms into the paraelectric cubic phase at still higher temperatures. Using group theoretical considerations, we show that the observed atomic displacements associated with this isostructural phase transition correspond to specific irreducible representations of the P4mm space group at its Brillouin zone center, and as such this transition may be phonon driven. Pronounced anomalies in the thermal displacement parameters at the T1 to T2 transition provide evidence for such a phonon-mediated isostructural phase transition. The high tetragonality ferroelectric phase (T1) of BF-0.31PT shows the largest NTE coefficient reported so far in the mixed BF-xPT system. The isostructural transition is shown to persist for tetragonal compositions of BF-xPT up to x = 0.60. A complete phase diagram of the BF-xPT system showing the existence of a critical point at T ∼ 677 K for x ≈ 0.63 is also presented.